Linkage of Optimization Models

Abstract

The general goal of this article is to investigate the question of how to carry out analysis when a set of mathematical models being used are interdependent. We seek systematic ways of linking such models to each other. The linking approaches should preserve the structure of the original models so that their interpretation during the analysis does not get increasingly complicated. Although the emphasis is on linking two interdependent linear programming models, extensions to multimodel, nonlinear, and stochastic cases can, in principle, be straightforward.

The article has been divided into two parts. In the first part we give a precise statement of our interdependent systems. As well, we offer three typical examples of such systems: energy supply--economy, manpower--economy, and forestry--wood processing industry interaction systems. In the second part we consider alternative approaches: classical decomposition principles, approaches derived from nondifferentiable optimization techniques, application of parametric programming techniques as well as the simplex method combined with a partitioning technique. By no means does the paper provide a final solution to our linkage problem. However, our computational experiments indicate that some of the approaches give rise to optimism, while others remain inconclusive.